I've got a 2 acre pond (stock tank here in Texas) about 100 yds directly behind my house, and another smaller tank about 400 yds to the northwest behind my house. The 2 acre pond is loaded with snapping turtles, and they're huge too!! The smaller tank has them too.
Only two ways to get rid of them that I know of. You either build or buy a turtle trap, as referenced in an earlier post, and buying will cost you approx $200.00 minimal, or you have fun in the evening and go shoot the boogers!!
As far as the stink with a trap, the stink doesn't last long, IF you have any vultures around, as they'll have a feast on them and leave you nothing but an empty shell, or pile of shells. Just dump the dead ones out of the trap somewhere away from your home or barn. If you have a bunch of turtles, you'll have to dump several loads. The traps actually drown the turtles and that's what kills them.
Shooting turtles with a 22 can be fun, but dangerous too, as the angle you shoot at determines if that bullet glances off the water and goes somewhere you don't want it to. Shooting them with a shotgun is a lot less dangerous.
Eating them, or finding someone that does, can get interesting and difficult. Don't go on a guilt trip if you can't, and just take care of business as it best suits you and your situation.
Don't worry, because you won't be eliminating turtles from the world. They'll walk a couple of miles, especially when it's dry, to get from one dry tank to one with water in it. I've watched them do that here many times.
Good Luck, and I'll be eliminating a bunch here pretty soon myself!! I know how you feel, especially if like me, you stock your pond with game fish and see those turtles eating them every day!!